Details

sample28.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results

6.0ms	51×	body	1280	valid
4.0ms	45×	body	640	valid
4.0ms	133×	body	80	valid
3.0ms	113×	body	80	nan
2.0ms	21×	body	320	valid
0.0ms	6×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.6b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
1.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 35

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series17.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sqrt (+ x 1.0))
14.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify31.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	282	318
1	1037	308
2	5001	297

prune74.0ms

Filtered

31 candidates to 41 candidates (-32.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	37	4	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.1b

Counts

42 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 80

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series20.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	514	800
1	2206	753
2	5001	721

prune157.0ms

Filtered

59 candidates to 89 candidates (-50.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	7	89
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 0.0b

Counts

93 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.0b	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

1122×	`*-un-lft-identity`
900×	`sqrt-prod`
774×	`times-frac`
460×	`distribute-lft-out`
294×	`add-sqr-sqrt`
292×	`add-cube-cbrt`
46×	`associate-/l*`
28×	`sqrt-div`
24×	`associate-/r/`
18×	`associate-/r*`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 547

Calls

4 calls:

8.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
15.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
30.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series48.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms	(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
18.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify127.0ms

Algorithm

egg-herbie

Counts

559 → 559

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1304	11535
1	5001	9913

prune678.0ms

Filtered

153 candidates to 559 candidates (-265.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	554	5	559
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	559	9	568

Merged error: 0b

Counts

568 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
0.3b	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
0.4b	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

2769×	`*-un-lft-identity`
2178×	`times-frac`
2070×	`sqrt-prod`
1090×	`distribute-lft-out`
1056×	`cbrt-prod`
796×	`add-sqr-sqrt` `add-cube-cbrt`
405×	`unpow-prod-down` `cube-prod`
64×	`sqrt-div`
60×	`associate-/r/`
46×	`associate-/l*`
45×	`cube-mult` `unpow3` `sqr-pow`
36×	`associate-/r*`
33×	`flip3-+` `flip-+`
30×	`div-inv`
12×	`add-exp-log`
10×	`add-cbrt-cube`
6×	`pow1` `cube-div`
4×	`cbrt-undiv` `cbrt-div` `div-exp` `add-log-exp`
3×	`pow-unpow` `pow-pow` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow1/3` `pow-exp` `sqrt-pow2` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 1360

Calls

4 calls:

13.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
52.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
9.0ms	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
9.0ms	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

series57.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms	(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)))
10.0ms	(cbrt (pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3))
19.0ms	(pow (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) 3)

simplify317.0ms

Algorithm

egg-herbie

Counts

1372 → 1372

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2277	34376
1	5002	29157

prune1.3s

Filtered

227 candidates to 1372 candidates (-504.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1370	2	1372
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	1372	9	1381

Merged error: 0b

Counts

1381 → 9

regimes298.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample829.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 23.520795%

Guaranteed chance to sample good point: 65.377249%

Results

216.0ms	1703×	body	1280	valid
130.0ms	1302×	body	640	valid
113.0ms	4147×	body	80	nan
112.0ms	4033×	body	80	valid
47.0ms	639×	body	320	valid
16.0ms	323×	body	160	valid

Details

sample28.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite11.0ms

series17.0ms

simplify31.0ms

prune74.0ms

localize7.0ms

rewrite24.0ms

series20.0ms

simplify65.0ms

prune157.0ms

localize10.0ms

rewrite108.0ms

series48.0ms

simplify127.0ms

prune678.0ms

localize14.0ms

rewrite235.0ms

series57.0ms

simplify317.0ms

prune1.3s

regimes298.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample829.0ms

Profiling